Superior ferroelectricity and nonlinear optical response in a hybrid germanium iodide hexagonal perovskite

Abundant chemical diversity and structural tunability make organic–inorganic hybrid perovskites (OIHPs) a rich ore for ferroelectrics. However, compared with their inorganic counterparts such as BaTiO3, their ferroelectric key properties, including large spontaneous polarization (Ps), low coercive field (Ec), and strong second harmonic generation (SHG) response, have long been great challenges, which hinder their commercial applications. Here, a quasi-one-dimensional OIHP DMAGeI3 (DMA = Dimethylamine) is reported, with notable ferroelectric attributes at room temperature: a large Ps of 24.14 μC/cm2 (on a par with BaTiO3), a low Ec below 2.2 kV/cm, and the strongest SHG intensity in OIHP family (about 12 times of KH2PO4 (KDP)). Revealed by the first-principles calculations, its large Ps originates from the synergistic effects of the stereochemically active 4s2 lone pair of Ge2+ and the ordering of organic cations, and its low kinetic energy barrier of small DMA cations results in a low Ec. Our work brings the comprehensive ferroelectric performances of OIHPs to a comparable level with commercial inorganic ferroelectric perovskites.

or valences. Thus 1D OIHPs are endowed with great structural freedom to engineer high-performance ferroelectrics with intriguing functionalities. Indeed, some 1D OIHP ferroelectrics have been synthesized and exhibit interesting properties such as large piezoelectric response 34 , multi-step nonlinear optical switches 35 , photoluminescence, magnetism 36 , and circularly polarized luminescence 37 . In particular, two 1D OIHP ferroelectrics [Me 3 NCH 2 Cl]MCl 3 (M = Mn and Cd) have been reported to show large piezoelectric response on par with BaTiO 3 38 . Even though, the comprehensive performances of available OIHP ferroelectrics remain incompetent when competing with conventional ferroelectric oxides. The most serious problems are their small P s (typically <10 μC/cm 2 ) and relatively high E c (~100 kV/cm). For comparison, the P s of BaTiO 3 reaches 26 μC/cm 2 and its typical E c is 10 kV/cm 39 .
Screening and modifying organic cations (imidazole, pyrrolidine, quinuclidine, etc.) are efficient strategies to improve the material performance 40 . Because the polarization switching of OIHPs is generally related to the ordering reorientation of organic cations, it appears that small organic cations may be beneficial in reducing the coercive field. Besides, the inorganic framework of BX 6 octahedra is also with remarkably compositional diversity. But their contributions to polarization have mostly been omitted since those octahedra formed by common transition metals (i.e., Cd, Cr, Mn, Cu) are generally inactive to ferroelectricity.
Inspired by the aforementioned ideas ( Supplementary Fig. 1), we used the small DMA + cation and germanium halide to synthesize a series of OIHP DMAGeX 3 (X = Cl, Br, I) (Supplementary Note 1). Remarkably, OIHP DMAGeI 3 exhibits excellent ferroelectricity with T C = 363 K, a high P s = 24.14 μC/cm 2 , and a low E c = 0.8-2.2 kV/cm at room temperature. To our best knowledge, such an experimental P s is higher than those of most reported pure-organic and inorganicorganic hybrid ferroelectrics, and rivals the popular ferroelectric oxide BaTiO 3 . And equally importantly, its E c value is one order of magnitude lower than that of recently reported inorganic perovskite CsGeI 3 (∼40 kV/cm) 41 , and two orders of magnitude lower than those of PVDF (∼500 kV/cm) and its copolymers 39 . Moreover, it owns a large SHG response, whose intensity is more than ten times stronger than that of KH 2 PO 4 (KDP, a commonly used standard system). Our finding brings the comprehensive performances of OHIP ferroelectrics to a comparable level with typical inorganic ferroelectric perovskites.

Structural analysis of crystal
Yellow and transparent rod-shaped single crystals of DMAGeI 3 in size of 2 × 2 × 16 mm 3 (Fig. 1a) were prepared by hydrothermal method (Supplementary Note 1). The phase purity and thermal stabilities of grown crystals were identified by powder X-ray diffraction (XRD) and thermogravimetric analysis (TGA), which shows good environmental and thermal stability ( Supplementary Figs. 2 and 3). Phase transition of DMAGeI 3 was characterized using differential scanning calorimetry (DSC) measurements. As shown in Supplementary Fig. 4, the DSC curves show a pair of thermal anomalies peaked at 359 K and 363 K in cooling/heating runs, respectively. For convenience, we defined the phase above T C of 363 K as the high-temperature phase (HTP) and the phase below T C as the low-temperature phase (LTP). Crystal structures in LTP and HTP were determined by variable-temperature singlecrystal X-ray diffraction in the range of 223-373 K (Supplementary Note 2 & Table 1).
The structural analysis discloses that DMAGeI 3 crystallizes in a centrosymmetric space group Pnan in HTP, while in LTP it transforms into a polar space group Pna2 1 . Figure 1b, c show that the two phases are similar except for the DMA orientation and GeI 3 distortion. DMAGeI 3 adopts the hexagonal perovskite structure containing 1D inorganic framework, where the GeI 3 units are linked via the facesharing GeI 6 octahedra. The cavities between GeI 3 columns are filled by organic DMA cations, which are loosely connected with the inorganic framework via N-H···I and C-H···I hydrogen bonding interactions. In HTP, the organic DMA cations locate at the 2-fold crystallographic rotation axes of lattice and exhibit orientational disorder toward two equivalent directions, making their dipole moments cancel each other (Fig. 1b). In LTP, the DMA cations become ordered with an aligned manner along the c-axis ( Fig. 1c and Supplementary Fig. 5), and also their positions move significantly (0.38 Å) along the c-axis direction compared with those in HTP ( Supplementary Fig. 6), both of which induce a net dipole moment in this direction (Fig. 1c). Concomitantly, the Ge-I bond lengths and I-Ge-I angles in LTP also changed obviously (Supplementary Fig. 7 and Supplementary Table 2), although the GeI 6 octahedra are already distorted in HTP. The value of the octahedron distortion parameter Δ and angle variance σ oct rise from 0.0096/60.6 (HTP) to 0.0121/69.3 (LTP) respectively, which reflect a more distorted state of GeI 6 octahedra in LTP (Supplementary Table 3).
These structural characteristics, including the orientation ordering of DMA cation, the structural distortion of GeI 3 framework, and the relative moving between these two parts, will contribute to a ferroelectric polarization along the c-axis, which will be further analyzed later.

Characterization of ferroelectricity
According to the above structural analysis, the symmetry breaking occurs with the change of space group from Pnan to Pna2 1 , and the symmetry elements halved from eight (E, C 2 , 2C 2 , i, σ h , and 2σ v ) to four (E, C 2 , and 2σ v ), which means the DMAGeI 3 is a mmmFmm2-type ferroelectric with two equivalent polarization directions 42 .
Second harmonic generation (SHG) experiment on powder sample was used to characterize its paraelectric-ferroelectric phase transition (Supplementary Note 2). As shown in Fig. 2a, DMAGeI 3 shows a strong SHG response at room temperature, which confirms its noncentrosymmetric LTP. With increasing temperature, the SHG signal intensity gradually decreases to zero above T C , indicating that the HTP structure is transformed into a centrosymmetric one. Moreover, the SHG measurement on a single crystal surface of DMAGeI 3 can further reveal the direction vector of ferroelectric polarization  Fig. 2b, the angle-dependent SHG intensity shows a clear bipolar behavior, namely its intensity reaches the maximum (minimum) when the polarization direction of incident light is parallel (perpendicular) to the spontaneous polarization direction (i.e., c-axis) of DMAGeI 3 crystal. It is worth to mention that the SHG strength of DMAGeI 3 (of power sample) is more than ten times that of KDP (Fig. 2a), comparable to that of previous reported hybrid halide antiperovskite Cs 3 Cl(HC 3 N 3 S 3 ) (11.4 × KDP) 45 , and better than many other reported ferroelectrics ( Fig. 2c and Supplementary Table 4). Thus, a direct application of DMAGeI 3 crystal is the nonlinear optical converter, which can omit bright green light via photoluminescence, as demonstrated in Supplementary Fig. 10.
Paraelectric-ferroelectric phase transition is generally accompanied by an obvious dielectric anomaly. The temperature-dependent dielectric real part (ε′) of DMAGeI 3 was measured on single crystals along three crystallographic axes at various frequencies. As shown in Fig. 2d, e, the dielectric constant along the c-axis (ε′ c ) is much larger than those along the other two axes, especially in the region around T C. This dielectric anisotropy can be ascribed to this mmmFmm2-type phase transition that only allows spontaneous polarization along the c-axis. It is noteworthy that the value of ε′ c reveals an obvious frequencydependence. Specifically, as the frequency decreases from 1 MHz to 1 kHz, the peak value of ε′ c at T C increases from 4679 to 102988 which is about 3269 times of its dielectric constant (~31.5) at room temperature ( Fig. 2e). To our knowledge, this is the largest dielectric response in the reported hybrid perovskite materials to date (Fig. 2f & Supplementary  Table 5). Additionally, according to the Curie-Weiss law, the C para and C ferro are calculated to be 9664 and 17469 K at 1 kHz, respectively. The ratio of C ferro /C para is 1.8 (smaller than 4), which discloses the characteristics of second-order ferroelectric phase transition (Supplementary Fig. 11).
The polarization-electric field (P-E) hysteresis loop is the most direct evidence of ferroelectricity. Figure 2g shows the P-E loops at various temperatures. Above T C (e.g., 373 K), the polarization response to the applied field presents almost linear behavior with a very narrow loop, while the well-defined P-E hysteresis loops were observed in the range of 343-303 K (below T C ), as expected for the paraelectricity and ferroelectricity of the HTP and LTP. As the temperature decreases in the LTP, both the saturation polarization (P s ) and remnant polarization (P r ) increase gradually, and reach up to 24.14 μC/cm 2 and 20.26 μC/cm 2 at 303 K, respectively. Remarkably, the P s of DMAGeI 3 is larger than The SHG intensity of DMAGeI 3 as a function of temperature on powder samples. Inset: the comparison of SHG signals between DMAGeI 3 and KDP powder samples (in the same range of particle diameter 300-450 μm) at room temperature. More comparisons with various particle sizes can be found in Supplementary Fig. 8, which leads the same conclusion. b The SHG anisotropic polar plot of DMAGeI 3 crystal, where the φ is the angle between the baxis and the polarization of incident light. c Comparison of SHG intensity between DMAGeI 3 and other ferroelectrics. d The temperature-dependent dielectric real part (ε′) of DMAGeI 3 measured on single crystals along the a, b, and c-axis at 1 kHz. e The temperature-dependent dielectric real part (ε′) of DMAGeI 3 measured on single crystals along the c-axis at various frequencies. f Comparison of the maximum value of ε′ of DMAGeI 3 and other ferroelectrics. g, h The typical polarizationelectric field (P-E) hysteresis loops measured along the c-aixs at various temperatures and at different frequencies.  38 , and very close to that of BaTiO 3 (Fig. 2i & Supplementary Table 6).
Another notable feature of DMAGeI 3 ferroelectricity is its small coercive field (E c ) values (0.8-2.2 kV/cm), which are one order of magnitude lower than that of the recently reported all-inorganic perovskite CsGeI 3 (∼40 kV/cm) 41 , and two orders of magnitude lower than those of PVDF (∼500 kV/cm) and its copolymers 39 . More comparisons with other hybrid ferroelectrics can be found in Supplementary  Table 7. Such a small E c is advantageous for energy-saving operations in devices. Furthermore, the polarization switching speed is also a key property for ferroelectric applications, thus the frequency dependence of P-E hysteresis loops is investigated, as shown in Fig. 2h. With rising frequency, the values of P s and P r slightly decrease, while the coercive voltage increases. Its ferroelectric polarization can be switched at a frequency up to 100 kHz, which shows excellent highfrequency performance for macroscopic crystals with large scale domains. Given the large P s value in combination with the small E c and the high-frequency performance, DMAGeI 3 represents promising hybrid ferroelectric materials for device applications. Moreover, the piezoelectric response has also been measured by using the quasistatic method. At room temperature, the d 33 of the DMAGeI 3 crystal reaches 3 pC/N, along the polar axis [001] under a testing frequency of 110 Hz (Supplementary Fig. 13).
For ferroelectrics, the microscale domain structure is another essential property of polarity, which can be characterized by using the piezoresponse force microscopy (PFM) technology 46 . By adjusting the lateral (in-plane) or vertical (out-of-plane) mode in PFM, the relative strength of piezoelectric response and polarization directions from different components can be harvested. Figure 3a, b display a schematic diagram of PFM in-plane testing on DMAGeI 3 crystal along the caxis (polarization direction), and the obtained topography of the crystal surface is shown in Fig. 3c. In the lateral mode, the observed obvious stripy domain walls parallel to the c-axis eliminate the interference of topography and confirm the existence of ferroelectric polarization (Fig. 3d). Combined with amplitude, the two sides of the domain wall show the response to different polarization directions, displaying obvious phase difference (Fig. 3e). In contrast, the piezoelectric signals do not give a component in the vertical direction ( Supplementary Fig. 14), verifying the results of crystal structure determination (mmmFmm2-type ferroelectric).
To further illustrate the ferroelectricity of DMAGeI 3 , the ferroelectric domain is switched using PFM. As shown in Fig. 3f, the butterfly-shaped amplitude (blue) and phase hysteresis loops (red) provide evidence for ferroelectric switching. A single domain state region with 30 × 30 μm 2 is selected to demonstrate the domain inversion of DMAGeI 3 (Fig. 3g). After applying positive bias of +50 V for 0.5 s, in the sectional area parallel to the c-axis on the right side of the point where the bias was applied, the polarization direction is switched (Fig. 3h). On the contrary, when giving a bias of −50 V for 0.5 s, the domain in the left area is reversed, resulting in the appearance of the stripy domain (Fig. 3i). Subsequently, a higher bias is applied to the center point, and the left area turns to the same phase, which is obviously different from the reverse polarization direction on the right (Supplementary Fig. 15). Our PFM measurement results strongly prove that DMAGeI 3 possesses stable and switchable polarization.

Discussion
To further understand the prominent ferroelectricity of DMAGeI 3 , we performed density-functional-theory (DFT) calculations to reveal underlying mechanisms. Our DFT calculation leads to lattice constants close to the experimental LTP one (Supplementary Fig. 17). And its electronic structure is shown in Supplementary Fig. 18, suggesting a good insulator with a band gap 2.79 eV. The valance band maximum is contributed by Ge and I. The theoretical value of polarization is estimated as 29.09 μC/cm 2 at the ground state (i.e., T = 0 K), which agrees well with (and slightly higher than) the experimental value at room temperature.
Then the ferroelectric origin of DMAGeI 3 is analyzed. First, the 4s 2 lone pair of Ge 2+ ion is a strong driving force of ferroelectricity, as appeared in the all-inorganic 3D perovskite CsGeI 3 41 . As illustrated in Fig. 4a, the 4s 2 lone pairs form a zigzag pattern along the inorganic chain, leading to an uncompensated dipole along the c-axis in the LTP. In contrast, in the HTP structure, the local dipoles from 4s 2 lone pairs are fully compensated, as compared in Fig. 4b. Second, besides the contribution from Ge 2+ 's 4s 2 lone pair, the effect of DMA cation is also non-negligible. Both the bodily movement of this +1 charged group and stereo orientation of this asymmetric structure will generate a local dipole. A simple estimation of their individual contributions are 16.18 μC/cm 2 (from the DMA cations) and 13.62 μC/cm 2 (from the GeI 3 framework) respectively (see Supplementary Note 3 and Supplementary Fig. 19). In other words, the large polarization of DMAGeI 3 is due to the synergistic effect of inorganic and organic parts, with almost halfhalf weights.
The ferroelectric switching process of DMAGeI 3 can be also simulated by rotating the DMA cations, as depicted in Fig. 4a. If the four DMA cations in one unit cell rotate synchronously, the switching barrier energy is 292.9 meV, which is not as low as expected. However, this barrier can be significantly reduced by rotating the DMA cations one by one, as compared in Fig. 4b, where the first and second barriers of the rotating steps are 109.6 meV and 115.6 meV, respectively. For comparison, the DFT switching barrier for a BaTiO 3 unit cell is~8.3 meV and its experimental coercive field E c is <10 kV/cm 12 . But it should be noted that the unit-cell volume of DMAGeI 3 is~16.5 times of BaTiO 3 . Thus, the two one-by-one barriers are only~6.6 meV and~7.0 meV for DMAGeI 3 when normalized to the volume of BaTiO 3 . Compared with BaTiO 3 , the proximate P s and lower barrier of DMAGeI 3 suggest an even smaller E c , as observed in our experiments.
Furthermore, its prominent SHG signal can be also well reproduced theoretically. The nonlinear optical susceptibility tensors (d ij 's) of LTP of DMAGeI 3 are calculated, which determine the intensity and anisotropy of SHG signals. For DMAGeI 3 with space group Pna2 1 , its SHG intensity on the bc crystalline plane can be expressed as 47 : I DMAGeI 3 / ð2d 24 sin 2φÞ 2 + ð2d 32 cos 2 φ + 2d 33 sin 2 φÞ 2 , where φ is the angle between the polarization direction of incident light and b-axis (more details can be found in Supplementary Note 4). As shown in Fig. 4c, the calculated SHG plot of DMAGeI 3 shows a bipolar behavior, and the strongest signal appears when the polarization direction of incident light is along the c-axis of crystal, consistent with the experimental observation.
For comparison, the d ij 's of KDP room temperature phase (space group I42d) is also calculated, which agrees well with the experimental values ( Supplementary Fig. 20). As expected, these values are systematically smaller than those of DMAGeI 3 . Thus the SHG signal of KDP is much smaller than that of DMAGeI 3 , since generally the SHG response is proportional to the square of d ij 's, as compared in Fig. 4c.
Our study unambiguously demonstrated the excellent comprehensive ferroelectric properties of DMAGeI 3 with quasi-onedimensional structure, which is a breakthrough of organicinorganic hybrid ferroelectrics as well as low-dimensional ferroelectrics. Its remarkable ferroelectricity originates from the synergistic overlap of two robust mechanisms: ordering of polar cations and soft mode of 4s 2 lone pairs, which doubles its net polarization and keeps its coercivity at a low level. This successful example provides a reliable and simple route to pursue more superior ferroelectrics or even multiferroics in organic-inorganic hybrid systems, to finally reach the aim of commercial applications. The opportunities are vast for emerging hybrid germanium halide perovskites, and the ones equipped with multipolar characteristics and outstanding piezoelectric performance may be available in the near future.

DSC, SHG, and XRD measurements
Differential scanning calorimetry (DSC) measurements were carried out by using a NETZSCH DSC 200F3 instrument under the nitrogen atmosphere, where the dry powder of DMAGeI 3 (28.9 mg) were heated and cooled with a rate of 10 K/min in the temperature ranges of 293-390 K. SHG switching experiments were measured with powder samples by pulsed Nd: YAG (1064 nm, Vibrant 355 II, OPOTEK), and the temperature varies from 300 K to 380 K. The powdered KH 2 PO 4 (KDP) was used as the reference. The SHG phase matching tests were performed with a particle size range of 62-375 μm at room temperature. Furthermore, the SHG intensity anisotropy was investigated by using Witec alpha 300 on single-crystal surfaces. Variabletemperature single-crystal X-ray diffraction data were collected on a Rigaku VarimaxTM DW diffractometer with Mo Kα radiation (λ = 0.71073 Å). Data processing with empirical absorption correction was conducted by using the CrysAlisPro 1.171.40.14e (Rigaku OD, 2018). The crystal structures were confirmed by direct methods and refined by full-matrix least-squares methods based on F 2 through the OLEX2 and SHELXTL (version 2018) software package. All non-hydrogen atoms were refined anisotropically and all hydrogen atoms were generated geometrically in suitable positions.

Dielectric and ferroelectric measurements
For the dielectric measurements, the sample of DMAGeI 3 was made with single-crystals cut perpendicular to the a-, b-, and c-axis respectively. Silver conduction paste deposited on the plate surfaces was used as the electrodes. The temperature-dependent dielectric constants were performed on the Tonghui TH2828A instrument under the frequency range from 1 kHz to 1 MHz with an applied electric field of 1 V. The single crystal electrodes of DMAGeI 3 were prepared for the P-E hysteresis loop measurements by Sawyer-Tower method. The ferroelectric polarization imaging and local switching studies on the bulk crystal surface were carried out by using a resonant-enhanced PFM (MFP-3D, Asylum Research).

PXRD and TGA measurements
Powder XRD data were measured using a Rigaku D/MAX 2000 PC X-ray diffraction system with Cu Kα radiation in the 2θ range of 5°-50°with a step size of 0.02°. The thermogravimetric analysis (TGA) were performed on the NETZSCH TG 209F3 instrument in the range of 298-1000 K with a heating rate of 20 K/min.

DFT Calculations
The electronic structure calculations were performed based on projector augmented wave pseudopotentials, as implemented in Vienna ab initio Simulation Package (VASP) 48 . Plane-wave cutoff energy of 500 eV and 3 × 4 × 4 k-point meshes were used. The lattice constants and the atomic positions were fully relaxed with the convergence criteria of 10 −5 eV and 0.01 V/Å for energy and force, respectively. The exchange-correlation potential was approximated in the form of Perdew-Burke-Ernzerhof (PBE) functional and the van der Waals (vdW) interaction was considered by adding D3 Grimme correction 49,50 . Other choices of functional and vdW correction were also tested ( Supplementary Fig. 17). The climbing nudged elastic band method was used to determine the paths and energy barrier of ferroelectric switching 51 . Ferroelectric polarization was calculated by using the Berry phase method 52 . The second-harmonic nonlinear optical susceptibility tensors for SHG were calculated using the exciting package 53 .
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